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COMEDK2024MathematicsIndefinite Integration

The value of e^ x^5 x^4 d x is

Options

  1. Ae^ x^5 +C
  2. B5 e^ x^5 +C
  3. Ce^ x^5 5 +C
  4. DNone of these

Correct answer

C. e^ x^5 5 +C

Step-by-step solution

Let x^5=t Differentiate both sides w.r.t. x , 5 x^4 d x =d tx^4 d x = d t 5 e^ x^5 x^4 d x = e^t d t 5 = 1 5 e^t d t [ e^t d t=e^t+C ]= 1 5 e^t+C= 1 5 e^ x^5 +C

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